Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories

The present paper is focused on the size-dependent shear buckling of nanoplates embedded in Winkler-Pasternak foundation and hygrothermal environment. Hence, the refined higher-order plate theories (Polynomial, Exponential, and Hyperbolic) needless of any shear correction factor are used in the formulations. The equations of motion are derived based on the mentioned theories in conjunction with the nonlocal strain gradient theory employing Hamilton's principle. The four unknown functions denoting the buckling load of plates are defined in a modal manner, and Navier solution method is used to find the shear buckling response. Results for the shear buckling and thermal buckling analysis of nanoplates are approved by existing literature to demonstrate the accuracy of present formulation and solution method. From our knowledge, it is the first time that the hygrothermal environment and also the nonlocal strain gradient theory are applied to study on shear buckling of nanoplates. Hence, the influence of nanoplate geometry, various hygrothermal conditions, elastic medium, nonlocal parameter and gradient parameter on the shear buckling load are obtained and discussed using different plate theories. The numerical results indicate that the shear buckling of nanoplate in the absence of strain gradient parameter is significantly affected by the temperature and moisture variations.